Thank you both very much! You guys just saved the day.. Using the info you generously provided, I put this simple diagram together.

This connector is attached to an OTTO PTT headset that I'd like to use with my Thales Liberty radio.
Assuming my diagram is correct, my plan is to disconnect this adapter and splice it to a 6-pin hirose cable I've attached to a Thales sidemate hirose/programming adapter.
My only two unknowns now are:
- which wires pass through the Thales adapter to the hirose connection (I plan to use a multimeter here)
- which wires I need to splice from the headset cable to the hirose cable
Here are photos of my setup, and the pinout to the Thales adapter:
Any guidance here would be greatly appreciated.